(Solved): 1. Orthogonal Matrices i. Identify a set of values \( a, b, c \) such that the columns of the foll ...

1. Orthogonal Matrices i. Identify a set of values \( a, b, c \) such that the columns of the following matrix are mutually orthogonal. \[ A=\left[\begin{array}{ccc} 1 & -1 & a \\ 1 & c & 2 \\ b & -1 & 1 \end{array}\right] \] ii. Calculate \( A A^{\top} \) iii. Use your answer in (i) to determine an orthogonal matrix \( B \) and verify that \( B^{\top}=B^{-1} \)